Rigs & RiggingJan 1, 2003
When it comes to the modern sailboat rig, there has been a definite design trend toward higher masts and shorter booms. This rigging choice is seen most clearly on racing machines, but it has also become a factor on the average voyaging boat.
There are, of course, advantages to this type of rig, but there are also some significant penalties. An examination of different rig styles reveals some of the trade-offs designers must make when drawing a voyaging rig.
The relationship of wingspan to wing breadth is termed "aspect ratio" and is expressed as a simple fraction. A kite has an aspect ratio of less than 1:1, while the lifting surfaces of all birds, aircraft, and modern sails are wider in span than chord.
Even though airplane wings show little variation among types designed for similar purposes, the sail plans of yachts embody a wide variety of individual sail shapes and even multiple-spar configurations. In terms of the efficiency of each individual sail, however, the primary concern is aspect ratio.Experiments have shown that no other factor has so great an effect upon the amount of power (lift) that can be generated from a cloth "wing" relative to various types of friction (drag) which are inescapable when the flow of air is changed by a foil.
It is useful to discuss sailboat aspect ratio in mainsails as basically the fraction of boom length to hoist, and in jibs as the projected foot length to hoist. This convention would only be correct, however, if all sails were perfect rectangles. True, the most critical factor in aspect ratio is the relation of height of mast to the foot of the sail. But there are permutations of sail planform shapeanything between nearly rectangular gaff rigs, to fully battened and theoretically ideal "elliptical" shapes, to the commonplace trianglethat have a major impact upon the actual, effective aspect ratio which, in turn, largely determines the efficiency of the rig.
For voyaging boats, the norm varies between a hoist-to-boom ratio in mainsails between 2:1 and 4:1. A somewhat greater variation exists in jibs: from genoas at 2:1 to blades and spitfire staysail jibs that are near 5:1. While ocean racers carry headsails of various aspect ratio, a voyager with roller furling headsails normally uses a jib with a complementary planform shape to the main. Thus arranged, there will be similar force produced by a boomed-out main and jib when sailing before the wind, causing little or no imbalance of force that would cause the boat to yaw off course. Although the preference for sloop rigs employing only two sails makes the subject simpler, it is interesting to consider other rigs. In fact, the broad spectrum of rigs includes many that are beneficial when aspect ratio is considered.
Once any airfoil is angled to a fluid flow, there will be a differential between pressure above and beneath the surface. With compressed molecules (high pressure) below and a low density of molecules (low pressure) above, some of the high pressure fluid will attempt to equalize the pressure difference by flowing around all edges. None can get around the sharp "trailing" edge, and hardly any can proceed "upstream" and around the front of a sheet of cloth set on a mast or stay. However, there isn't much to prevent significant flow out around the "sides." (In practice, heavy aircraft flying at highly-loaded angles of attack will produce a tremendous continuous swirl of air flowing around their wing tips, the notorious wingtip vortex which can disastrously interfere with smaller aircraft in their wake.)
Of course, a sailboat's wing extends only in one direction, up aloft, and the deck effectively stops any vortex that wants to circulate beneath a jib or main boom. Still, a major loss of pressure will occur at the top of a sail, and the constant vortex there will be the primary limitation upon your sailboat's "wind-engine." Escaping pressure
Two things happen when air escapes around the ends of a wing. First, there is a "leak" of pressure differential between the two sides, which translates into less power or lift generated by the airfoil. Secondly, much of the energy that creates a swirl of air around the outer ends of the foil ends up in the "drag" category. Most of it translates indirectly into "induced" drag, the kind of drag that results from angling the wing to the oncoming air. The more air that leaks around the ends, the more angle of attack is needed in order to achieve a selected amount of lift, and this will cause a longer backwards (drag) vector in the simple diagram of lift and drag.
If we have negative effects on both lift and drag resulting from activity at the ends of a wing, foil or sail, then it only makes sense to make the ends smaller in relation to the whole. In a rectangular lifting surface, it is generally correct to say that the less "side" or "wingtip" proportional to leading edge, the smaller will be the pressure losses (and drag increases) for the entire wing. So, any rectangular lifting foil will perform better the longer and narrower one can make it. The difference in performance results mainly from diminished drag, not necessarily increased lift. A wide variety of foil shapes, given equal surface area, will generate fairly similar amounts of maximum lift. But the surface with the high aspect ratio will produce far less drag.
Early aircraft designers realized that evolution had nearly perfected birds for flying; their wings were tapered and rounded at the ends. It wasn't long before designers devised a structure that mimicked this shape. They found that this created more lift and less drag. In the clear vision of hindsight, it seems obvious that it would be better to taper a wing towards the tip, since this will artificially increase the ratio of leading and trailing edges, and resist pressure losses, while minimizing the wingtip. A long skinny triangle (much like a Marconi mainsail or blade jib) would seem a clever trick, its apex being a single point and thus an infinitely small wingtip. This was tried experimentally, but wind tunnels made it clear that fluid began to flow turbulently from the high pressure side to the low as loading increased out near the ends. Clearly, some taper was good, but it could easily be overdone.
An early researcher in aerodynamics, Ludwig Prandtl, experimented with various wing shapes and found that induced drag became minimal relative to lift when pressure over the entire foil from its root to its tip could be plotted as a quarter-ellipse. Pressure per unit area could be modified in several ways, but the two most applicable to sails were by twisting the foil (called "wash" by wing designers) or by continually diminishing the area of the wing near the ends. Since wing warping or "wash" proved both difficult and expensive, diminishing the loading was usually handled in aircraft by just rounding off the wing.
Elliptical wings were created in an attempt to match surface area to the ideal pressure gradient. Thus, we can understand their existence on a whole generation of aircraft (and a short-lived generation of racing boat keels). Further experimentation disclosed that it was possible to achieve "elliptical" patterns of load distribution without the foil actually being elliptical: A tapered but square-ended foil works just as well but uses less material. Virtually all modern aircraft now use such tapered wing shapes.
The upshot of all this experimentation was an important change in the way aspect ratio was calculated, because the advantage of wing shaping became clear. The numerical formula for aspect ratio used in aerodynamics will produce a higher aspect ratio in wings of equal length if there is taper, rounding-off, or a combination of both. For sailors, the lesson is significant. It means that a hollow-leached main that stows inside the mast is a very different animal from a fully battened, high-roach model. Even if they both set on masts and booms of identical measure (and thus would conventionally be considered among sailors to be of the same aspect ratio) they have very different effective aspect ratios, as calculated using pure aerodynamics. One may be nearly a third more effective than the other in similar conditions!Practical limits
A discussion of the relative merits of high and low aspect ratio for the offshore sailor is far more complex than the same science as it applies to airplane wings. The reason for this is twofold:
1) The aspect ratio and ultimate length of an aircraft wing are limited by little other than the strength of the material of which they're made. Gliders would probably have spectacular wingspans of 70 feet or more if materials were available with the necessary strength. On a sailboat, however, there are several constraints that rein in aspect ratio, primarily hull stability, but also concerns about mast height. These range from spar strength to rigging windage right down to the height of fixed bridges. Additionally, there are sailcloth limitations, control of twist, convenient furling, reefing, handling, and maintenance, just to name a few.
2) Airplanes are designed to operate at all times in an unstalled condition (although stall characteristics are a consideration.) Sailboats, however, use their air foils in far more diverse ways. Much of the time a sail acts exactly like a wing, operating at an angle of attack between a few degrees to almost 20, with air flowing relatively smoothly from luff to leach. But when broad reaching or on a dead run, their angle to the approaching air is excessive and flow becomes entirely stalled. Complicating matters, on a dead run, it is commonplace for tailwinds to reach the leech first and flow in reverse toward the mast, or, in the case of an unvanged main, proceed in one direction aloft and the opposite near deck level.
It would be tempting to definitively state that tall, thin sails are best upwind. However, it is impossible to isolate aspect ratio entirely from its effect upon a boat's sail plan. As sails get taller, their center of effort goes higher (CE is that place on the sail where, by averaging, all the vectors of force are considered to act). A large part of recent discussions about aspect ratio in sailing publications has confused aspect ratio with center of effort, but this is excusable because of the link between them. The height of a rig is limited more by the need to keep it upright than anything else, therefore, aspect ratio and total area are impossible to consider without reference to a hull's stability.
Unquestionably, given enough stability, the most efficient sailsuntil stalledwill be tall and narrow. Every designer knows that for about three quarters of the speed polar from beating to broad reaching, when air flows smoothly over the sails without stalling, a sail will produce more force and less drag if it is tall and narrow. But there is obviously a practical limit on the height of the boat's total combined center of sail effort, which is dependent upon stability. Since CE goes up with span, angles of heel can occur in monohulls that more than overcome any advantage gained from increased lift. In practice, this means the sailor will have to reef to go as fast. But his reefed vessel, with its diminished sail area and (at best) useless windage above the sail, will be less effective than a lower aspect ratio rig that might have been able to continue underway at full hoist. Of lesser importance, but certainly pertinent, is the effect of high CE on rolling and steering yaw, which increase somewhat as sailplans are elevated. Stability plays a part
The relationship of stability and center of effort as it relates to aspect ratio is important in another way. Aspect ratio is important in comparing wings, stalled or not, that have equal area. But any wing, stalled or not, will create lift proportional to its size. As one lowers center of effort through aspect ratio, the boat's heeling moment is lessened, leaving one free to generously increase the total spread of sail. Because the low aspect ratio rig can be increased in size (sail area), there is a wide arc of points of sail when it will beat the necessarily smaller, higher-aspect rig. Especially when running for long periods, for instance on a tradewinds circumnavigation, the lower rig can be far superior if it is much larger in area. Taken to an extreme, one could broad reach with an enormous horizontal rectangular sail, whose area would be almost completely effective, were one able to keep it from dipping in the ocean with even minor rolling. (Wild speculation among voyagers even considers the deployment of low aspect ratio kites to high altitudes, where the winds blow strong and smooth, tethered with carbon fiber line to a low point at the bow!)
It is clear that a voyager's perspective on the subject must take into account both his boat's stiffness and the proportion of offwind work intended. There may, indeed, be voyagers who will achieve better practical performance for their itinerary with a large, squat rig for the tradewinds and a large, powerful diesel for the few times they expect to go to windward. The fact is that while aspect ratio is a critical factor in the handling and performance of sailplans, there are few boats whose sail shape was specifically optimized for offshore sailing. The great majority of boats found voyaging are "stock" racer-cruisers. Although their hulls might have been sensibly laid out to go the distance, their sails were often defined to some extent by the need to win races for sales-related publicity. This would normally force the aspect ratio up for several reasons. Boats intended to club race will have been configured in consideration of handicap rules. All rules penalize sail area, so the designer will want to produce the smallest total square footage. Still, the theory of aspect ratio insists that a tall and thin foil produces the most efficient force per unit of area. Of course, the handicap formula takes aspect ratio into account, too, penalizing higher ratios. But it is the opinion of the vast majority of designers (expressed through their actual boats) that there are other factors, the wind gradient being just one example, which conspire toward the desirability of high aspect ratio.
One factor that is strongly counter to a voyager is that racing designs have tall rigs with the expectation that a maximum number of crew will be sitting on the rail. In fact, this gambit has been taken so far that modern rules actually have to place a limit upon the weight of crew carried in races. Needless to say, the ocean voyager has no interest in enlisting a cadre of linebackers to suffer on the rail day and night in order to get the most out of a towering rig.
There is one way to achieve the beating and reaching efficiency of higher aspect ratio while keeping the whole rig's center of effort low. That is to "split" the rig into more than one foil, spread out along the hull. Although this trick reached an extreme in the seven-masted schooner Thomas W. Lawson, it is most often expressed in two-masted cruisers like schooners, ketches, and yawls. Unfortunately, here is a case when theory butts up against practice. The penalty paid by high center of effort is great, and, unquestionably, placing several long, thin foils along the length of a vessel looks great on paper.
However, the flow off one sail can either enhance, or interfere with, the effectiveness of another. Take the example of beating. With only two sails, main and jib, the interrelationship is beneficial more often than not. But with a second mast, beating becomes more problematic: by the time the jib has achieved force by curving the airflow and the main has taken that altered flow and sapped a little more energy by curving it some more, the poor mizzen is presented with air from almost directly ahead. In a well-designed yawl, this isn't as bad as it seems, since the mizzen can be furled, and the remaining sail plan will still provide effective driving force. Ketches, however, fare worse when beating, since they place more reliance on the mizzen for actual power. The schooner is the worst of all upwind, since it places more reliance on the aftermost sails, the ones that have to work with poor flow angles.
On a reach, however, the theoretical advantage of several higher-aspect foils spread out along the hull works out. But running again causes interference problems, with the aft sails blocking flow for those ahead.
What conclusion can voyagers draw about the optimum aspect ratio? For the most part, it depends on several factors: How much time will one be sailing in conditions when the sails will not be stalled? If the answer is plenty, then how much of this sailing will be close-hauled, when the hull's stability is an important factor?
The place to start may be with an accurate appraisal of hull stability in relation to the sail height and area. There are several formulas familiar to naval architects that do just that (Dallenbaugh angle, Letcher angle, etc.). These will actually predict an angle of heel in a specific wind strength and can be applied by comparison with many other known boats. They are most useful for the designer starting from scratch, because he or she can produce a new boat with a predictable amount of stiffness, tweaking the aspect ratio as high as possible for the customer's heel-happiness.
The owner of an existing boat will have to balance weatherliness with stability, making changes to cure whichever is in deficit. Many ploys can make available the upwind advantage of higher aspect ratio, such as carbon masts, rod rigging, the lowering of weights aboard, water ballast, or by making more efficient boom-to-mast dimensions via a fully battened (more elliptical-tipped) main. The latter gives higher effective aspect ratio with the same, or even a shorter, mast.
Voyagers should take a sanguine look at their sails and rig. If the main and jib have shrunk, as older dacron sails often do, there will have been a loss of effective aspect ratio. Take a look, also, at the height of boom above deck. It should be as low as possible, since it will dam the flow beneath, while increasing the effectiveness of the sail. The limiting safety factor is a low boom in the cockpit.
Bear in mind that the leading edge of the sails produces more lift than the leach. Very fast boats, from BOC racers to Bahamian racing sloops, tack the main right at deck level while the boom goes high to clear the crew aft. It is only a matter of time until someone invents a "pusher" vang, which attaches from the boom upward to the mast. Then, the only detriment of this sort of rig (extreme sail twist) will be eliminated, producing even higher useful aspect ratio in modern sailboat mainsails.
Fully raised sails
At the other extreme (aloft), this discussion must make clear the importance of making sure the sails go truly full-hoist. It is useless to carry bare mast or headstay above the top of the sails. From deck level, sails may appear to be fully up, but a view from another boat or the dock usually reveals a fair gap between head and sheave. This can be corrected in two ways. If the boat is tender, then leave the sails as they are and shorten the mast, because this pays benefits in terms both of hull stability and parasite windage aloft. But if the boat is stiff, then add to the sails in order to take advantage of every inch of rig height. On a stable platform, the best aspect ratio is the highest possible through a wide arc of points of sail.
There is another category, encompassing voyagers who either expect to be sailing predominately downwind (sails stalled), or who don't really give a hoot about the last half-knot under sail. Again, given that their boat has adequate stability to be safe, one could argue in favor of adding sail area while retaining the existing mast heightby lengthening the boom or at least assuring that the mainsail is capable of outhauling to its very end. Lots of sail area concentrated down low is just the ticket for offwind voyaging. I might add that in all my years of delivering yachts, the most comfortable and confident trips were in the lowest-aspect boats, certainly not the racers. One can always avoid light air, or motor through it. And any voyager can choose to get a little more upwind performance via rod rigging, stowing all those red jerry cans belowdecks, running the chain rode into a box under the fore-berthor replacing a small two-blade prop with a large folding or feathering model that will make motorsailing against a breeze more thinkable.
Certainly most newer yachts will give one the upwind benefits of a higher aspect ratio rig. Given sufficient stiffness, the northeast corner of a boat's speed polars can be pushed to the maximum via a high-aspect rig. But many voyagers prefer to sail one of the tempting bargains crowding the used boat marketpocketing the difference in a bloated cruising kitty. Older boats, in many cases, don't have the righting moment to contemplate heightened aspect ratio.
The preceding analysis reveals that older boats with low-aspect rigs can be just as fast broad reaching the trade winds and may well be better running. While they are limited in their ability to sail off a lee shore, they'll be more comfortable and more manageable much of the time.
Art Paine is a professional yacht captain, boat builder, designer, writer, and photographer living in Bernard, Maine.